Dodecagon
From Wikipedia, the free encyclopedia
In geometry, a dodecagon is a polygon with exactly twelve sides. When spelled uppercase, the outlines of the letters E and H (and I in a slab serif font) are all dodecagons.
A regular dodecagon is a dodecagon with all sides having equal length and all interior angles having the same size of 150 degrees. The area of a regular dodecagon is given by: <math>A = 3 a^2 \cot \frac{\pi}{12} = 3 a^2 \left( 2+\sqrt{3} \right) \simeq 11.1962 a^2.</math>
Alternately, <math>A = 3 r^2 \frac{}{}</math> where r is the radius of a circumscribed circle.
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[edit] Dodecagon construction
A regular dodecagon is constructible with compass and straightedge. The following is a 23 step animation illustrating one way it can be done. Notice that the compass radius is unaltered during steps 8 through 11.
[edit] Tilings with dodecagons
| Image:Tile 3bb.svg Semiregular tiling 3.12.12 | Image:Tile 46b.svg Semiregular tiling: 4.6.4.12 |  A demiregular tiling: 3.3.4.12 & 3.3.3.3.3.3 |
[edit] Dodecagons in real life
- The Australian 50-cent coin Fijian 50-cent, Tongan 50-seniti and Solomon Island 50-cent coin is 12-sided. Until July 2005, a Romanian coin (5000 ROL) was also dodecagonal. The Canadian penny was dodecagonal from 1982 to 1996 as well as the South Vietnamese 20 Ðong coin till 1975. Zambian 50 ngwee (till 1992) and Malawian 50 tambala (till 1995) coins were dodecagonal.
[edit] See also
[edit] External links
- Dodecagon and Kurschak's Tile and Theorem by Antonio Gutierrez from "Geometry Step by Step from the Land of the Incas"
- Weisstein, Eric W., Dodecagon at MathWorld.
- Kürschak's Tile and Theorem
- Definition and properties of a dodecagon With interactive animation
| Polygons |
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| Triangle | Quadrilateral | Pentagon | Hexagon | Heptagon | Octagon | Enneagon (Nonagon) | Decagon | Hendecagon | Dodecagon | Triskaidecagon | Pentadecagon | Hexadecagon | Heptadecagon | Enneadecagon | Icosagon | Icosihenagon | Tricontagon | Pentacontagon | Hectagon | Chiliagon | Myriagon |
